Need some help for an experiment (Eye animation)
From the texture provided in your question, you can use &quot;uv warp&quot; modifier to do this:

How to do it:

UV unwrap the eye part that will be textured.
Place this UV part over the texture part you want: move and scale (big pupil, for instance)
Add the &quot;UV warp&quot; modifier.
The modifier uses two objects, say empties. One is the base, the other one &quot;empty.001&quot; is the one to shift from the base.


Move the empty so that its position and scale makes the UV cover the wanted part of the texture.
Keyframe it when the position is ok.
Do it for all steps of your animation.
Then, go to the graph editor to edit the empty movement to constant steps.

The corresponding shader node tree:


Note: if the background is not pink but white as the eye is, you can add some more variations, as done here: How can I move a UV Island to simulate the Movement of an Eye